Proposition 2.4 ([1]} Section 3) 
Let \(E,F,G\)  be subspaces of \(\mathcal {B}\)  of the same finite \(k\) -dimension, and \(A,B:\mathcal {B}\rightarrow \mathcal {B}\)  be bounded linear maps for which \(AE\subset F\) , \(BF\subset G\) .
Then:
